Lizzie came up with a divisibility test for a certain number :\(m\)

Break a positive integer \(n\) into two-digit chunks, starting from the ones place. (For example, the number \( 354764\) would break into the two-digit chunks \(64,47,35\) )

Find the alternating sum of these two-digit numbers, by adding the first number, subtracting the second, adding the third, and so on. (In our example, this alternating sum would be \(64-47+54=52.\))

Find m and show that this is indeed a divisibility test for m (by showing that n is divisible by m if and only if the result of this process is divisible by m).

Guest Feb 18, 2021